We have the vector field $F(x,y) = (\frac{-y}{x^2 + y^2} , \frac{x}{x^2 + y^2})$
I want to check if this vector field is conservative in $D = ℝ^2 - (0,0) $. Is it enough to check for equality between the partial derivative with respect to y for the first component and the partial derivative with respect to $x$ for the second component or does the domain pose problems for this method?